Question

What values of x and y satisfy the system of equations
{8x+9y=−3
{6x+7y=1

Answer 1

A) 8x + 9y = -3
B) 6x + 7y=1
We multiply A) by -(6/8)
A) -6x -6.75y = 2.25 then we add this to
equation B
B) 6x + 7y=1
25y = 3.25
y = 13
and X=-15
^ 5.0
Explanation:

Answer 2

• Let's first assign identifications to the equations given:

`{ \rm{8x + 9y = {}^( - )3 \: - - - \{equation \: (a) \} }} \\ { \rm{6x + 7y = 1 - - - \{equation \: (b) \}}} \\`

• There are various methods to solve this system of equation, namely;

1. Graphical method
2. Substitution method
3. Elimination method
4. Calculus (Calculator synthetic method)

1. Graphical method

→ You'll have to draw a graph, demacate it very well following the suitable scale.

→ Get values to plot from both equation (a) and equation (b).

→ Draw respective lines of each equation. The point of intersection of the lines is the answer of the values of x and y.

→ It'll be in coordinate format i.e; (x, y)

2. Substitution method

→ Lemme first consider equation (a)

`{ \rm{8x + 9y = {}^( - )3 }}`

• make x the subject of the equation (a):

`{ \rm{8x = - 3 - 9y}} \\ \\ { \rm{x = ( - 3)/(8) - (9)/(8)y }} \: { \rm{- - - \{equation \: (c)}} \}`

→ Considering equation (b) next

`{ \rm{6x + 7y = 1}}`

• substitute x in equation (b) with x in equation (c)

`{ \rm{6( ( - 3)/(8) - (9)/(8)y ) + 7y = 1 }} \\ \\ { \rm{ - (9)/(4) - (27)/(4) y + 7y = 1}} \\ \\ { \rm{ (1)/(4) y = (13)/(4) }} \\ \\ { \underline{ \rm{ \: \: y = 13 \: \: }}}`

• then find x using equation (c)

`{ \rm{x = ( - 3)/(8) - (9)/(8) y }} \\ \\ { \rm{x = ( - 3)/(8) - (9)/(8) (13)}} \\ \\ { \underline{ \rm{ \: \: x = - 15 \: \: }}}`

3. Elimination method:

→ Here, we have to align the equations so that if we use addition or subtraction operations we remain with one term giving us zero [ eliminated ]

→ Multiply equation (a) by 6 and multiply equation (b) by 8. In order to eliminate x

→ Then we subtract equation (a) with equation (b)

`{ \underline{ \rm{ - \binom{6(8x + 9y = - 3)}{8(6x + 7y = 1)} }}} \\ { \rm{ 0x \: - 2y = - 26 }} \\ \\ { \rm{ - 2y = - 26}} \\ \\ { \underline{ \rm{ \: \: y = 13 \: \: }}}`

• find x using equation (c)

`{ \rm{x = ( - 3)/(8) - (9)/(8) y}} \\ \\ { \underline{ \rm{ \: \: x = - 15 \: \: }}}`

4. Calculator synthetic method:

→ To use this method, you must have a scientific calculator.

→ If you have it, follow the steps below;

• Go to mode (press it 3 times until you see "EQN" )
• Press 1 or any number below the "EQN". It'll display "Unknowns" with 2 and 3 below it. 2 → Two equations system. 3 → 3 equations system.
• According to our question, it is a two equations system, press 2
• It'll display a, b and c [ a is the coefficient of x, b is the coefficient of y, c is the constant]
• For a1 press 8 then press "equal sign", b1 press 9, then equal sign, c1 press -3 then equal sign.

• Follow the same procedure for a2, b2 and c2
• Automatically, It will display the answers

Answer: x = -15, y = 13